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Aldrichyang
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Tyro
Asked: 2021-04-08T14:23:57+00:00 In: ,

MEAN, VARIANCE, STANDARD DEVIATION OF BINOMIAL

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Eyeglassomatic manufactures eyeglasses for different retailers. In March 2010, they tested to see how many defective lenses they made, and there were 16.9% defective lenses due to scratches. Suppose Eyeglassomatic examined twenty eyeglasses.

  • Find the mean.
  • Find the variance.
  • Find the standard deviation
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1 Answer

  2. acedstud

    Let X be a random variable representing the number of defective lenses, then X describes a binomial distribution with n=20 and p=16.9\%=0.169.

    • The mean of a binomial distribution is given by \mu=np=20\times0.169=3.38.
    • The variance of a binomial distribution is given by \sigma^2=np(1-p)=20\times0.169\times(1-0.169)=20\times0.169\times0.831=2.80878.
    • The standard deviation of a binomial distribution is given by \sigma=\sqrt{np(1-p)}=\sqrt{2.80878}\approx1.676.

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